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Asymptotic properties of bridge estimators in sparse high-dimensional regression models

The Annals of statistics, ISSN 0090-5364, 2008, Volume 36, Issue 2, pp. 587 - 613

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to...

Zero | Sample size | Objective functions | Mathematical constants | Regression analysis | Coefficients | Orthogonality | Estimators | Consistent estimators | Oracles | High-dimensional data | Penalized regression | Asymptotic normality | Oracle property | Variable selection | asymptotic normality | NONCONCAVE PENALIZED LIKELIHOOD | P2/N | BEHAVIOR | high-dimensional data | oracle property | STATISTICS & PROBABILITY | variable selection | NORMALIZATION | PARAMETERS | penalized regression | 2-WAY SEMILINEAR MODEL | 62J05 | 62J07 | 62E20 | 60F05

Zero | Sample size | Objective functions | Mathematical constants | Regression analysis | Coefficients | Orthogonality | Estimators | Consistent estimators | Oracles | High-dimensional data | Penalized regression | Asymptotic normality | Oracle property | Variable selection | asymptotic normality | NONCONCAVE PENALIZED LIKELIHOOD | P2/N | BEHAVIOR | high-dimensional data | oracle property | STATISTICS & PROBABILITY | variable selection | NORMALIZATION | PARAMETERS | penalized regression | 2-WAY SEMILINEAR MODEL | 62J05 | 62J07 | 62E20 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 6/2009, Volume 37, Issue 3, pp. 1150 - 1171

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and...

Cosmic microwave background radiation | Isotropy | Central limit theorem | Astrophysics | Approximation | Spherical harmonics | Milky Way Galaxy | Polynomials | Statistics | Angular separation | High-frequency asymptotics | Tests for Gaussianity and isotropy | Random fields | Spherical needlets | random fields | tests for Gaussianity and isotropy | central limit theorem | SPHERES | spherical needlets | STATISTICS & PROBABILITY | WAVELETS | GAUSSIANITY | Probability | Mathematics | 62G20 | 62M40 | 60F17 | 60F05

Cosmic microwave background radiation | Isotropy | Central limit theorem | Astrophysics | Approximation | Spherical harmonics | Milky Way Galaxy | Polynomials | Statistics | Angular separation | High-frequency asymptotics | Tests for Gaussianity and isotropy | Random fields | Spherical needlets | random fields | tests for Gaussianity and isotropy | central limit theorem | SPHERES | spherical needlets | STATISTICS & PROBABILITY | WAVELETS | GAUSSIANITY | Probability | Mathematics | 62G20 | 62M40 | 60F17 | 60F05

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 01/2016, Volume 53, Issue 1, pp. 141 - 160

Spectral measures of Wigner matrices are investigated. The Wigner semicircle law for spectral measures is proved. Regard this as the law of large number, the...

MATHEMATICS | 15A52 | 60F05

MATHEMATICS | 15A52 | 60F05

Journal Article

The Annals of probability, ISSN 0091-1798, 9/2009, Volume 37, Issue 5, pp. 1778 - 1840

We consider n x n real symmetric and Hermitian Wigner random matrices $n^{-1/2}W$ with independent (modulo symmetry condition) entries and the (null) sample...

Statistical variance | Interpolation | Cauchy Schwarz inequality | Central limit theorem | Statistical theories | Eigenvalues | Fourier transformations | Mathematical moments | Random variables | Covariance matrices | Linear eigenvalue statistics | Random matrix | linear eigenvalue statistics | central limit theorem | FLUCTUATIONS | STATISTICS & PROBABILITY | CLT | FUNCTIONALS | Mathematics - Probability | 15A52 | 62H99 | 60F05

Statistical variance | Interpolation | Cauchy Schwarz inequality | Central limit theorem | Statistical theories | Eigenvalues | Fourier transformations | Mathematical moments | Random variables | Covariance matrices | Linear eigenvalue statistics | Random matrix | linear eigenvalue statistics | central limit theorem | FLUCTUATIONS | STATISTICS & PROBABILITY | CLT | FUNCTIONALS | Mathematics - Probability | 15A52 | 62H99 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 2010, Volume 38, Issue 2, pp. 1122 - 1170

Given a sample from some unknown continuous density $f\colon {\Bbb R}\rightarrow {\Bbb R}$ , we construct adaptive confidence bands that are honest for all...

Integers | Density estimation | Minimax | Covariance | Mathematical functions | Random variables | Density | Mathematical maxima | Estimators | Confidence interval | Wavelet estimators | Kernel estimators | Extremes | Gaussian processes | Adaptive estimation | Limit theorem | INEQUALITIES | APPROXIMATION | NONPARAMETRIC REGRESSION | STATISTICS & PROBABILITY | extremes | limit theorem | RATES | GAUSSIAN-PROCESSES | kernel estimators | SETS | ADAPTATION | REGIONS | CONVERGENCE | INTERVALS | density estimation | wavelet estimators | 62G07 | 60F05

Integers | Density estimation | Minimax | Covariance | Mathematical functions | Random variables | Density | Mathematical maxima | Estimators | Confidence interval | Wavelet estimators | Kernel estimators | Extremes | Gaussian processes | Adaptive estimation | Limit theorem | INEQUALITIES | APPROXIMATION | NONPARAMETRIC REGRESSION | STATISTICS & PROBABILITY | extremes | limit theorem | RATES | GAUSSIAN-PROCESSES | kernel estimators | SETS | ADAPTATION | REGIONS | CONVERGENCE | INTERVALS | density estimation | wavelet estimators | 62G07 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 2004, Volume 32, Issue 6, pp. 2385 - 2411

The term "sequential Monte Carlo methods" or, equivalently, "particle filters," refers to a general class of iterative algorithms that performs Monte Carlo...

Monte Carlo methods | Central limit theorem | Filtration | Approximation | Algorithms | Particle density | Bayesian Methodology | Mathematical functions | Data smoothing | Weighting functions | Genetic algorithms | Residual resampling | Recursive Monte Carlo filter | Resample-move algorithms | State-space model | Markov chain Monte Carlo | Particle filter | residual resampling | resample-move algorithms | APPROXIMATION | STABILITY | state-space model | STATISTICS & PROBABILITY | recursive Monte Carlo filter | particle filter | Statistics | Mathematics | 65C05 | 82C80 | 62F15 | 60F05 | 62L10

Monte Carlo methods | Central limit theorem | Filtration | Approximation | Algorithms | Particle density | Bayesian Methodology | Mathematical functions | Data smoothing | Weighting functions | Genetic algorithms | Residual resampling | Recursive Monte Carlo filter | Resample-move algorithms | State-space model | Markov chain Monte Carlo | Particle filter | residual resampling | resample-move algorithms | APPROXIMATION | STABILITY | state-space model | STATISTICS & PROBABILITY | recursive Monte Carlo filter | particle filter | Statistics | Mathematics | 65C05 | 82C80 | 62F15 | 60F05 | 62L10

Journal Article

Journal of applied probability, ISSN 0021-9002, 12/2007, Volume 44, Issue 4, pp. 889 - 900

Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {X ij , j ≥ 1}, i = 1,…,k. In this paper we...

Research Papers | Sums of random variables | Loss process | Consistently varying tail | Large deviation | sums of random variables | 60F10 | consistently varying tail | 60G50 | loss process | 60F05

Research Papers | Sums of random variables | Loss process | Consistently varying tail | Large deviation | sums of random variables | 60F10 | consistently varying tail | 60G50 | loss process | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 4/2015, Volume 43, Issue 2, pp. 903 - 934

The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the...

Bias correction | Threshold choice | Tail dependence | Multivariate extreme value theory | PROBABILITY | bias correction | MODELS | STATISTICS | ESTIMATORS | STATISTICS & PROBABILITY | INDEX | tail dependence | PICKANDS DEPENDENCE | threshold choice | Statistics | Statistics Theory | Mathematics | 62G05 | 62G20 | 60G70 | 62G32 | 60F05

Bias correction | Threshold choice | Tail dependence | Multivariate extreme value theory | PROBABILITY | bias correction | MODELS | STATISTICS | ESTIMATORS | STATISTICS & PROBABILITY | INDEX | tail dependence | PICKANDS DEPENDENCE | threshold choice | Statistics | Statistics Theory | Mathematics | 62G05 | 62G20 | 60G70 | 62G32 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2015, Volume 43, Issue 6, pp. 2537 - 2564

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We...

Point processes | Neuroscience | Randomization | Permutation | U-statistics | Independence test | Bootstrap | Spike train analysis | spike train analysis | EVENTS | randomization | neuroscience | point processes | STATISTICS & PROBABILITY | bootstrap | SAMPLES | HIGH DIMENSION | permutation | Statistics | Statistics Theory | Mathematics | 60G55 | 62P10 | 62M07 | 62F40 | 62E20 | 60F05

Point processes | Neuroscience | Randomization | Permutation | U-statistics | Independence test | Bootstrap | Spike train analysis | spike train analysis | EVENTS | randomization | neuroscience | point processes | STATISTICS & PROBABILITY | bootstrap | SAMPLES | HIGH DIMENSION | permutation | Statistics | Statistics Theory | Mathematics | 60G55 | 62P10 | 62M07 | 62F40 | 62E20 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 2/2015, Volume 43, Issue 1, pp. 238 - 275

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are...

MCMC | Markov chain monte carlo | Optimal scaling | Pseudo-marginal random walk metropolis | Particle methods | Diffusion limit | particle methods | DIFFUSION LIMITS | Markov chain Monte Carlo | pseudo-marginal random walk Metropolis | WEAK-CONVERGENCE | PARTICLE FILTERS | STATISTICS & PROBABILITY | CHAINS | optimal scaling | diffusion limit | 65C40 | 65C05 | 60F05

MCMC | Markov chain monte carlo | Optimal scaling | Pseudo-marginal random walk metropolis | Particle methods | Diffusion limit | particle methods | DIFFUSION LIMITS | Markov chain Monte Carlo | pseudo-marginal random walk Metropolis | WEAK-CONVERGENCE | PARTICLE FILTERS | STATISTICS & PROBABILITY | CHAINS | optimal scaling | diffusion limit | 65C40 | 65C05 | 60F05

Journal Article

The Annals of probability, ISSN 0091-1798, 1/2005, Volume 33, Issue 1, pp. 177 - 193

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance...

Brownian motion | Mathematical sequences | Mathematical theorems | Central limit theorem | Infinity | Chaos theory | Mathematical integrals | Mathematical inequalities | Random variables | Perceptron convergence procedure | Weak convergence | Brownian sheet | Multiple stochastic integrals | Fractional Brownian motion | multiple stochastic integrals | WIENER | EXPANSIONS | STATISTICS & PROBABILITY | fractional Brownian motion | weak convergence | FUNCTIONALS | Mathematics - Probability | 60H05 | 60F05

Brownian motion | Mathematical sequences | Mathematical theorems | Central limit theorem | Infinity | Chaos theory | Mathematical integrals | Mathematical inequalities | Random variables | Perceptron convergence procedure | Weak convergence | Brownian sheet | Multiple stochastic integrals | Fractional Brownian motion | multiple stochastic integrals | WIENER | EXPANSIONS | STATISTICS & PROBABILITY | fractional Brownian motion | weak convergence | FUNCTIONALS | Mathematics - Probability | 60H05 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2009, Volume 37, Issue 5A, pp. 2543 - 2560

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of...

Extracorporeal membrane oxygenation | Probability distributions | Proportions | Asymptotic properties | Clinical trials | Random allocation | Experimentation | Design efficiency | Allocative efficiency | Martingales | Urn model | Clinical trial | Doubly adaptive biased coin design | Biased coin design | Response-adaptive designs | Power | clinical trial | PROGNOSTIC FACTORS | doubly adaptive biased coin design | ASYMPTOTIC PROPERTIES | STATISTICS & PROBABILITY | ALLOCATION | SEQUENTIAL CLINICAL-TRIALS | biased coin design | PLAY-WINNER RULE | VARIABILITY | urn model | BIASED COIN DESIGNS | URN MODELS | power | 60F10 | 62G10 | 60F05 | 60F15

Extracorporeal membrane oxygenation | Probability distributions | Proportions | Asymptotic properties | Clinical trials | Random allocation | Experimentation | Design efficiency | Allocative efficiency | Martingales | Urn model | Clinical trial | Doubly adaptive biased coin design | Biased coin design | Response-adaptive designs | Power | clinical trial | PROGNOSTIC FACTORS | doubly adaptive biased coin design | ASYMPTOTIC PROPERTIES | STATISTICS & PROBABILITY | ALLOCATION | SEQUENTIAL CLINICAL-TRIALS | biased coin design | PLAY-WINNER RULE | VARIABILITY | urn model | BIASED COIN DESIGNS | URN MODELS | power | 60F10 | 62G10 | 60F05 | 60F15

Journal Article

The Annals of probability, ISSN 0091-1798, 2009, Volume 37, Issue 6, pp. 2150 - 2173

In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially...

Statistical variance | Gaussian distributions | Approximation | Statistical theories | Mathematical vectors | Matrices | Random variables | Covariance matrices | Statistics | Multivariate normal approximation | Stein's method | Exchangeable pairs | exchangeable pairs | multivariate normal approximation | CONVERGENCE | STATISTICS & PROBABILITY | CLT | CENTRAL-LIMIT-THEOREM | Mathematics - Probability | Stein’s method | 60F05 | 62E17

Statistical variance | Gaussian distributions | Approximation | Statistical theories | Mathematical vectors | Matrices | Random variables | Covariance matrices | Statistics | Multivariate normal approximation | Stein's method | Exchangeable pairs | exchangeable pairs | multivariate normal approximation | CONVERGENCE | STATISTICS & PROBABILITY | CLT | CENTRAL-LIMIT-THEOREM | Mathematics - Probability | Stein’s method | 60F05 | 62E17

Journal Article

Stochastic processes and their applications, ISSN 0304-4149, 2016, Volume 126, Issue 9, pp. 2634 - 2664

Chen (2001) derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process. We extend Chen’s...

Convergence rate | Branching random walk | Central limit theorems | Random environment in time | STATISTICS & PROBABILITY | Probability | Mathematics

Convergence rate | Branching random walk | Central limit theorems | Random environment in time | STATISTICS & PROBABILITY | Probability | Mathematics

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2007, Volume 35, Issue 5, pp. 2106 - 2142

We consider estimation in a particular semiparametric regression model for the mean of a counting process with "panel count" data. The basic model assumption...

Maximum likelihood estimation | Estimation bias | Maximum likelihood estimators | Mathematical functions | Sampling bias | Regression analysis | Poisson process | Estimators | Estimation methods | Perceptron convergence procedure | Counting process | Asymptotic normality | Consistency | Pseudo-likelihood estimators | Monotone function | Maximum likelihood | Empirical processes | Asymptotic efficiency | Information matrix | Asymptotic distributions | asymptotic distributions | information matrix | TESTS | monotone function | STATISTICS & PROBABILITY | asymptotic efficiency | MODEL | consistency | counting process | RECURRENT EVENTS | asymptotic normality | REGRESSION-ANALYSIS | maximum likelihood | pseudo-likelihood estimators | empirical processes | 60J65 | 60J70 | 60F17 | 60F05

Maximum likelihood estimation | Estimation bias | Maximum likelihood estimators | Mathematical functions | Sampling bias | Regression analysis | Poisson process | Estimators | Estimation methods | Perceptron convergence procedure | Counting process | Asymptotic normality | Consistency | Pseudo-likelihood estimators | Monotone function | Maximum likelihood | Empirical processes | Asymptotic efficiency | Information matrix | Asymptotic distributions | asymptotic distributions | information matrix | TESTS | monotone function | STATISTICS & PROBABILITY | asymptotic efficiency | MODEL | consistency | counting process | RECURRENT EVENTS | asymptotic normality | REGRESSION-ANALYSIS | maximum likelihood | pseudo-likelihood estimators | empirical processes | 60J65 | 60J70 | 60F17 | 60F05

Journal Article

The Annals of probability, ISSN 0091-1798, 11/2007, Volume 35, Issue 6, pp. 2294 - 2320

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear...

Approximation | Central limit theorem | Mathematical theorems | Stochastic processes | Stationary processes | Mathematical inequalities | Random variables | Logarithms | Martingales | Probabilities | Linear process | Nonlinear time series | Strong convergence | Law of the iterated logarithm | Martingale | Strong invariance principle | Short- and long-range dependence | APPROXIMATION THEOREMS | MOMENT INEQUALITIES | ITERATED RANDOM FUNCTIONS | MAXIMAL INEQUALITY | STATIONARY-PROCESSES | MIXING SEQUENCES | STRONG LAWS | PARTIAL-SUMS | STATISTICS & PROBABILITY | LINEAR-PROCESSES | CENTRAL-LIMIT-THEOREM | Mathematics - Probability | law of the iterated logarithm | nonlinear time series | martingale | linear process | 60F17 | strong convergence | strong invariance principle | 60F05

Approximation | Central limit theorem | Mathematical theorems | Stochastic processes | Stationary processes | Mathematical inequalities | Random variables | Logarithms | Martingales | Probabilities | Linear process | Nonlinear time series | Strong convergence | Law of the iterated logarithm | Martingale | Strong invariance principle | Short- and long-range dependence | APPROXIMATION THEOREMS | MOMENT INEQUALITIES | ITERATED RANDOM FUNCTIONS | MAXIMAL INEQUALITY | STATIONARY-PROCESSES | MIXING SEQUENCES | STRONG LAWS | PARTIAL-SUMS | STATISTICS & PROBABILITY | LINEAR-PROCESSES | CENTRAL-LIMIT-THEOREM | Mathematics - Probability | law of the iterated logarithm | nonlinear time series | martingale | linear process | 60F17 | strong convergence | strong invariance principle | 60F05

Journal Article

Probability surveys, ISSN 1549-5787, 2011, Volume 8, Issue 1, pp. 210 - 293

Journal Article

The Annals of applied probability, ISSN 1050-5164, 10/2015, Volume 25, Issue 5, pp. 2535 - 2562

We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time...

Second-order BSDEs | Numerical scheme | Robustness of BSDE | Weak approximation | robustness of BSDE | STATISTICS & PROBABILITY | weak approximation | numerical scheme | 93E15 | 65C50 | 60F05

Second-order BSDEs | Numerical scheme | Robustness of BSDE | Weak approximation | robustness of BSDE | STATISTICS & PROBABILITY | weak approximation | numerical scheme | 93E15 | 65C50 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2006, Volume 34, Issue 4, pp. 1827 - 1849

We investigate the properties of the Benjamini-Hochberg method for multiple testing and of a variant of Storey's generalization of it, extending and...

P values | Multiple Testing Problems | Proportions | Expected values | Goodness of fit | Perceptron convergence procedure | False discovery rate | Multiple testing | Empirical distributions | empirical distributions | RATES | multiple testing | STATISTICS & PROBABILITY | goodness of fit | false discovery rate | MULTIPLE TESTING PROCEDURES | 62J15 | 62G30 | 60F05

P values | Multiple Testing Problems | Proportions | Expected values | Goodness of fit | Perceptron convergence procedure | False discovery rate | Multiple testing | Empirical distributions | empirical distributions | RATES | multiple testing | STATISTICS & PROBABILITY | goodness of fit | false discovery rate | MULTIPLE TESTING PROCEDURES | 62J15 | 62G30 | 60F05

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2009, Volume 37, Issue 5B, pp. 2696 - 2729

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear...

Climate change | Precipitation | Time series | Stationary processes | Mathematical functions | Random variables | International environmental cooperation | Data smoothing | Estimators | Martingales | Smoothing | Local linear regression | Local stationarity | Bahadur representation | Global warming | Quantile estimation | Nonstationary nonlinear time series | nonstationary nonlinear time series | STATISTICS & PROBABILITY | quantile estimation | global warming | local linear regression | REGRESSION QUANTILES | KERNEL | MODELS | VARIABLES | local stationarity | smoothing | climate change | 62G05 | 60F05

Climate change | Precipitation | Time series | Stationary processes | Mathematical functions | Random variables | International environmental cooperation | Data smoothing | Estimators | Martingales | Smoothing | Local linear regression | Local stationarity | Bahadur representation | Global warming | Quantile estimation | Nonstationary nonlinear time series | nonstationary nonlinear time series | STATISTICS & PROBABILITY | quantile estimation | global warming | local linear regression | REGRESSION QUANTILES | KERNEL | MODELS | VARIABLES | local stationarity | smoothing | climate change | 62G05 | 60F05

Journal Article

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